Neural systems often have significant components of their behavior that appear to be random. Traditionally this randomness is modeled in stochastic and often linear terms. Since neural systems consist of highly interconnected nonlinear elements, however, a natural alternative explanation is that the randomness derives from complex nonlinear dynamics such as chaos. This has been suggested by experiments on several neural systems, including irregular firing patterns in the nervous systems of gastropod molluscs, the human electroencephalogram in deep sleep and epilepsy, single neuron recordings in the cat and monkey visual cortex, and hippus in the pupil-light reflex. However, inmost cases the evidence for chaos remains inconclusive, in large part because the data analysis is based on techniques that are notoriously unreliable, such as currently popular algorithms for computing fractal dimension. We have recently introduced a new approach to the analysis of experimental data, which is based on the identification of good features through nonlinear generalizations of principal component analysis, and the construction of nonlinear mappings using nonparametric techniques such as local approximation. These nonlinear mappings can be used for several purposes, including prediction, noise reduction, and system characterization. For time series data (e.g. sequences of interspike intervals) they provide more accurate and reliable methods for measuring fractal dimension and determining whether chaos is present. For stimulus- response experiments (e.g. event related potentials and fields) they can be used to search for regularity and predictability, both for classification and generalization. We propose to develop further our methods to cope with problems encountered in biological neural data, such as nonstationary behavior, and to apply our methods to data from neuroscience experiments including those listed above. This will allow us to determine with much more precision than has been achieved so far whether the apparent randomness of many neural phenomena derives from complex nonlinear dynamics. If indeed this is the case, then the result might be a significant change in the paradigm used for modeling the nervous system. If this is not the case, then we can avert pointless further work in this direction. Our ultimate purpose is to discover any underlying deterministic structure that may currently lie hidden in apparently random neural phenomena.